## Geometry & Topology

### Skeleta of affine hypersurfaces

#### Abstract

A smooth affine hypersurface $Z$ of complex dimension $n$ is homotopy equivalent to an $n$–dimensional cell complex. Given a defining polynomial $f$ for $Z$ as well as a regular triangulation $T△$ of its Newton polytope $△$, we provide a purely combinatorial construction of a compact topological space $S$ as a union of components of real dimension $n$, and prove that $S$ embeds into $Z$ as a deformation retract. In particular, $Z$ is homotopy equivalent to $S$.

#### Article information

Source
Geom. Topol., Volume 18, Number 3 (2014), 1343-1395.

Dates
Revised: 19 December 2013
Accepted: 17 January 2014
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732797

Digital Object Identifier
doi:10.2140/gt.2014.18.1343

Mathematical Reviews number (MathSciNet)
MR3228454

Zentralblatt MATH identifier
1326.14102

Subjects
Primary: 14J70: Hypersurfaces
Secondary: 14R99: None of the above, but in this section

#### Citation

Ruddat, Helge; Sibilla, Nicolò; Treumann, David; Zaslow, Eric. Skeleta of affine hypersurfaces. Geom. Topol. 18 (2014), no. 3, 1343--1395. doi:10.2140/gt.2014.18.1343. https://projecteuclid.org/euclid.gt/1513732797

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